(1) RFCMatchBoundsTRSProof (EQUIVALENT transformation)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
The following rules were used to construct the certificate:
a__f(f(a)) → a__f(g(f(a)))
mark(f(X)) → a__f(X)
mark(a) → a
mark(g(X)) → g(mark(X))
a__f(X) → f(X)
The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
311233, 311234, 311235, 311237, 311238, 311236, 311239, 311240, 311241, 311242
Node 311233 is start node and node 311234 is final node.
Those nodes are connect through the following edges:
- 311233 to 311234 labelled a__f_1(0), a(0), f_1(0), f_1(1)
- 311233 to 311235 labelled g_1(0)
- 311233 to 311236 labelled a__f_1(0), f_1(1)
- 311233 to 311239 labelled a__f_1(1), f_1(2)
- 311234 to 311234 labelled #_1(0)
- 311235 to 311234 labelled mark_1(0), a__f_1(1), a(1), f_1(2)
- 311235 to 311242 labelled g_1(1)
- 311235 to 311239 labelled a__f_1(1), f_1(2)
- 311237 to 311238 labelled f_1(0)
- 311238 to 311234 labelled a(0)
- 311236 to 311237 labelled g_1(0)
- 311239 to 311240 labelled g_1(1)
- 311240 to 311241 labelled f_1(1)
- 311241 to 311234 labelled a(1)
- 311242 to 311234 labelled mark_1(1), a__f_1(1), a(1), f_1(2)
- 311242 to 311242 labelled g_1(1)
- 311242 to 311239 labelled a__f_1(1), f_1(2)